/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 60 Find the standard form of the eq... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 60

Find the standard form of the equation of the parabola with the given characteristics. Focus: (0,0)\(;\) directrix: \(y=8\)

Short Answer

Expert verified
The standard form of the equation of the parabola is \(x^2 = 16(y+4)\)

Step by step solution

01

Determine the vertex

The vertex of a parabola is the point exactly between the directrix and the focus. In this case, since the focus is at (0,0) and the directrix is \(y=8\), we can calculate the vertex as being the midpoint between these two, which is \((0, -4)\).
02

Calculate 'a'

Using the vertex and focus, we can figure out the value of 'a' which is the distance between the vertex and the focus. In this case, it's the distance from \((0, -4)\) to \((0, 0)\), which is 4.
03

Write the equation

Now that we have the vertex and 'a', we can write down the equation of the parabola. Since it opens upward, the equation will be in the form \[x^2 = 4ay\], with (h, k) being the vertex. Plugging in the vertex and 'a', we find the equation to be \[(x-0)^2 = 4*4(y - -4)\] simplifies to \(x^2 = 16(y+4)\].

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use a graphing utility to graph the ellipse. Find the center, foci, and vertices. (Recall that it may be necessary to solve the equation for \(y\) and obtain two equations.) \(3 x^{2}+4 y^{2}=12\)

A simply supported beam is 12 meters long and has a load at the center (see figure). The deflection of the beam at its center is 2 centimeters. Assume that the shape of the deflected beam is parabolic. (a) Write an equation of the parabola. (Assume that the origin is at the center of the deflected beam.) (b) How far from the center of the beam is the deflection equal to 1 centimeter?

An __________ is the set of all points \((x, y)\) in a plane, the sum of whose distances from two distinct fixed points, called _______ is constant.

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(\frac{x^{2}}{4 / 9}+\frac{(y+1)^{2}}{4 / 9}=1\)

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(9 x^{2}+25 y^{2}-36 x-50 y+60=0\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.